On the Flux Conjectures
On the Flux Conjectures
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关于通量猜想
DOI：
10.1090/crmp/015/04
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
L. Polterovich
中科院分区：
文献类型：
--
作者：
F. Lalonde;D. Mcduff;L. Polterovich
关于辛流形的“流量猜想”指出，哈密顿微分同胚群在所有辛微分同态群中是C^1闭的。我们证明了关于球面有理流形和2-球面上的最小陈数为零或足够大的流形的猜想。我们还证实了辛环作用量的通量猜想的一个自然版本。在某些情况下，我们可以进一步证明哈密尔顿微分同胚群在所有辛微分同胚群的单位分量中是C^0闭的。
The ``Flux conjecture'' for symplectic manifolds states that the group of Hamiltonian diffeomorphisms is C^1-closed in the group of all symplectic diffeomorphisms. We prove the conjecture for spherically rational manifolds and for those whose minimal Chern number on 2-spheres either vanishes or is large enough. We also confirm a natural version of the Flux conjecture for symplectic torus actions. In some cases we can go further and prove that the group of Hamiltonian diffeomorphisms is C^0-closed in the identity component of the group of all symplectic diffeomorphisms.